Problem: Takahashi loves sorting.

He has a permutation (p_1,p_2,...,p_N) of the integers from 1 through N. Now, he will repeat the following operation until the permutation becomes (1,2,...,N):

* First, we will define high and low elements in the permutation, as follows. The i-th element in the permutation is high if the maximum element between the 1-st and i-th elements, inclusive, is the i-th element itself, and otherwise the i-th element is low.
* Then, let a_1,a_2,...,a_k be the values of the high elements, and b_1,b_2,...,b_{N-k} be the values of the low elements in the current permutation, in the order they appear in it.
* Lastly, rearrange the permutation into (b_1,b_2,...,b_{N-k},a_1,a_2,...,a_k).



How many operations are necessary until the permutation is sorted?

Constraints

* 1 ≤ N ≤ 2×10^5
* (p_1,p_2,...,p_N) is a permutation of the integers from 1 through N.

Input

Input is given from Standard Input in the following format:


N
p_1 p_2 ... p_N


Output

Print the number of operations that are necessary until the permutation is sorted.

Examples

Input

5
3 5 1 2 4


Output

3


Input

5
5 4 3 2 1


Output

4


Input

10
2 10 5 7 3 6 4 9 8 1


Output

6

Solution (in CPP):

Solution:
#include<bits/stdc++.h>

const int N = 200010;

int a[N], p[N], f[N], ans[N];
int n;

int main(){
	scanf("%d", &n);
	for (int i = 1; i <= n; ++ i){
		scanf("%d", &a[i]);
		p[a[i]] = i;
	}
	for (int i = n; i; -- i){
		if (!ans[i + 1]){
			if (i == n || p[i] < p[i + 1]){
				continue;
			}
			ans[i] = 1;
			f[i] = i + 1;
			continue;
		}
		if (p[f[i + 1]] < p[i] && p[i] < p[i + 1] || p[i] < p[i + 1] && p[i + 1] < p[f[i + 1]] || p[i + 1] < p[f[i + 1]] && p[f[i + 1]] < p[i]){
			ans[i] = ans[i + 1];
			f[i] = f[i + 1];
		}
		else{
			ans[i] = ans[i + 1] + 1;
			f[i] = i + 1;
		}
	}
	return printf("%d\n", ans[1]), 0;
}